WEIGHTED VARIABLE EXPONENT SOBOLEV SPACES WITH ZERO BOUNDARY VALUES AND CAPACITY ESTIMATES

Year 2018, Volume: 36 Issue: 2, 373 - 388, 01.06.2018

Cihan Ünal İsmail Aydın

Abstract

In this paper, we define weighted variable exponent Sobolev space with zero boundary values and investigate some properties of this space with weighted variable Sobolev capacity. We obtain Poincaré inequality with respect to zero boundary values. We will introduce a capacity in sense to this defined space and, also, give several estimates.

Keywords

Weighted variable exponent Sobolev spaces, Sobolev capacity, energy integral.

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